Chemical Swarming

Nano- and micro-scale objects can undergo autonomous motion owing to chemical activity at their surfaces – so-called catalytic nanomotors.  A surface chemical reaction creates local concentration gradients of the reactant (the fuel) and product species and, as these species diffuse in an attempt to re-establish equilibrium, they entrain the motor causing it to move.  A single chemically active particle acts as a source (or sink) creating a reactant concentration disturbance that decays as 1/r, where r is the distance from the active particle.  A second particle will, in general, undergo normal diffusiophoresis in the concentration gradient created by the first particle.  For particles that move down the concentration gradient two sink particles will attract each other, while two source particles will repel each other.  (A source and a sink particle will not move relative to one another.)  Thus, a collection of source particles will tend repel each other and drift apart, while sink particles will attract each other and tend to 'collapse' into a dense clump – they 'swarm.'  However, if fuel is supplied uniformly at the rate at which it is consumed by the active particles a 'chemically neutral' steady sate can be achieved in which the active particles exhibit Debye-like screening and phase behaviors analogous to those of a one-component plasma.